Synopses & Reviews
An unparalleled collection, this volume features 566 problems plus answers. They cover a wide range of topics in an accessible manner, including steady-state harmonic oscillations, the Fourier method, and the eigenfunction method for solving inhomogeneous problems. More advanced problems deal with integral transforms, curvilinear coordinates, and integral equations. 1965 edition.
Synopsis
This book is an unparalleled collection of worked problem material in applied mathematics consisting of 566 problems and answers impossible to find in any other single source. Covering a wide range of topics in a particularly accessible manner, the problems apply many different mathematical methods to questions drawn from mechanics, the theory of heat conduction, and the theory of electric and magnetic phenomena.
The first five chapters are suitable for anyone with a minimal background in applied mathematics. Topics covered are the derivation of equations and formulation of problems, some special methods for solving hyperbolic and elliptic equations, steady state harmonic oscillations, the Fourier method, and the eigenfunction method for solving inhomogeneous problems. The remaining three chapters are suitable for students with a more advanced background. These more complicated problemsdeal with integral transforms, curvilinear coordinates, and integral equations. Certain problems indicated throughout the text are solved in detail in a solutions section at the end of the text chapters. Included are a mathematical appendix and a supplement by Prof. E. L. Reiss titled "Variational and Related Methods," containing 51 additional problems, most with solutions. A particularly complete and valuable bibliography is also included.
This volume is another inthe popular series of fine translations from the Russian by RichardA. Silverman, formerly ofthe Courant Institute of Mathematical Sciences of New York University. Students of applied mathematics and scientists whose researches require its use will find this book invaluable. Teachers will find it an exceptional sourcebook of problems.
"Ijudge this to be a useful . . . book, and one well worthreprinting. It collects a considerable amount of material that would otherwise be available only from rather scattered sources." Jack Schwartz, Courant Institute of Mathematical Sciences, N.Y.U.
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Synopsis
566 problems and answers impossible to find in any other single source. Topics include steady-state harmonic oscillations, the Fourier method, and the eigenfunction method for solving inhomogeneous problems. More advanced problems deal with integral transforms, curvilinear coordinates, and integral equations. Detailed solutions.
Synopsis
Unparalleled collection of 566 problems and answers, impossible to find in any other single source. Supplement, with 51 additional problems, by Edward L. Reiss. Translated by Richard Silverman. 159 figures.
Synopsis
These 566 problems plus answers cover a wide range of topics in an accessible manner, including steady-state harmonic oscillations, Fourier method, integral transforms, curvilinear coordinates, integral equations, and more. 1965 edition.
Description
Bibliography: p. 415-422.
Bibliography: p. 415-422.
Table of Contents
Part 1 PROBLEMS
1 DERIVATION OF EQUATIONS AND FORMULATION OF PROBLEMS
1. Mechanics
2. Heat Conduction
3. Electricity and Magnetism
2 SOME SPECIAL METHODS FOR SOLVING HYPERBOLIC AND ELLIPTIC EQUATIONS
1. Hyperbolic Functions
2. Elliptic Equations: The Green's Function Method
3. Elliptic Equations: The Method of Conformal Mapping
3 STEADY-STATE HARMONIC OSCILLATIONS
1. Elastic Bodies: Free Oscillations
2. Elastic Bodies: Forced Oscillations
3. Electromagnetic Oscillations
4 THE FOURIER METHOD
1. "Mechanics: Vibrating Systems, Acoustics"
2. "Mechanics: Statics of Deformable Media, Fluid Dynamics"
3. Heat Conduction: Nonstationary Problems
4. Heat Conduction: Stationary Problems
5. Electricity and Magnetism
5 THE EIGENFUNCTION METHOD FOR SOLVING INHOMOGENEOUS PROBLEMS
1. Mechanics: Vibrating Systems
2. Mechanics: Statics of Deformable Media
3. Heat Conduction: Nonstationary Problems
4. Heat Conduction: Stationary Problems
5. Electricity and Magnetism
6. INTEGRAL TRANSFORMS
1. The Fourier Transform
2. The Hankel Transform
3. The Laplace Transform
4. The Mellin Transform
5. Integral Transforms Involving Cylinder Functions of Imaginary Order
7. CURVILINEAR COORDINATES
1. Elliptic Coordinates
2. Parabolic Coordinates
3. Two-Dimensional Bipolar Coordinates
4. Spheroidal Coordinates
5. Paraboloidal Coordinates
6. Toroidal Coordinates
7. Three-Dimensional Bipolar Coordinates
8. Some General Problems on Separation of Variables
8. INTEGRAL EQUATIONS
1. Diffraction Theory
2. Electrostatics
PART 2 SOLUTIONS
MATHEMATICAL APPENDIX
1. Special Functions Appearing in the Text
2. Expansions in Series of Orthogonal Functions
3. Some Definite Integrals Frequently Encountered in the Applications
4. Expansion of Some Differential Operators in Orthogonal Curvilinear Coordinates
Supplement. VARIATIONAL AND RELATED METHODS
1. Variational Methods
1.1 Formulation of Variational Problems
1.2 The Ritz Method
1.3 Kantorovich's Method
2. Related Methods
2.1 Galerkin's Method
2.2 Collocation
2.3 Least Squares
3. References
BIBLIOGRAPHY
NAME INDEX
SUBJECT INDEX